k-Distance Signed Total Domination Number of Graphs

International Conference on Algebra and Discrete Mathematics on January 8 to 10, 2018 Department of Mathematics, DDE, Madurai Kamaraj University, Tamil Nadu, India. International Journal of Computer Science (IJCS) Published by SK Research Group of Companies (SKRGC)

Abstract

Let G be a finite and simple graph with the vertex set V=V(G) of order n and edge set E=E(G). If v is a vertex of a graph G, the open k-neighborhood of v, denoted by Nk(v). A function f:V(G)?{?1,+1} is a k-distance non-negative signed total dominating function (k-DNNSTDF) of a graph G, if for every vertex v?V, f(Nk(v))= ?u?Nk(v) f(u)?0. The k-distance non-negative signed total domination number (k-DNNSTDN) of a graph G equals the minimum weight of a k-DNNSTDF of G, denoted by ?NNk,st(G). We study some properties of k-DNNSTDN in graphs and some families of graphs such as cycles, paths, complete graphs, star graphs and wheel graphs which admit 2-DNNSTDF.

References

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Keywords

signed total dominating function, k-distance non-negative signed total dominating function.